The uncertainty category 1) related to variability in demonstrations can be accounted for in the proposed framework through GP covariance, but we note this can produce unsafe impedance skills when the low demonstration variance arises from contact with the environment [1]}. The proposed framework also addresses the uncertainty category 2) related to confidence in skill by leveraging on GP model uncertainty in cost function and optimization constraints. The uncertainty category 3) related to environment constraints is handled by the increase in GP covariance induced by fitting hyperparameters on data with contact variance. An additional frequency-domain perturbation model is used to resolve the uncertainty category 4) related to external perturbations. The uncertainty category 5) related to human goal estimation is addressed by taking the expectation over the belief in human goal, inferred from the GP.
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